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On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize | ||
| Computational Methods for Differential Equations | ||
| مقاله 6، دوره 5، شماره 4، دی 2017، صفحه 324-347 اصل مقاله (236.94 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Truong Nguyen-Ba* ؛ Thierry Giordano؛ Remi Vaillancourt | ||
| Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 | ||
| چکیده | ||
| Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for considering this class of formulae is to obtain a set of $k$-step methods which are $L$-stable and are suitable for the integration of stiff differential systems whose Jacobians have some large eigenvalues lying close to the imaginary axis with negative real part. The approach, described in the present paper, allows us to develop $L$-stable $k$-step methods of order up to 10. Selected HBO($p$) of order $p$, $p=9,10$, compare favorably with existing Cash $L$-stable second derivative extended backward differentiation formulae, SDEBDF($p$), $p=7,8$ in solving problems often used to test stiff ODE solvers. | ||
| کلیدواژهها | ||
| Hermite--Birkhoff methods؛ generalized DIRK methods؛ $A$-stable؛ oscillatory stiff DETEST problems؛ confluent Vandermonde-type systems | ||
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